An account of Joanna Southcott's funeral appears in many newspapers, but the version below is from the Manchester Mercury of Tuesday 17th January 1815, as it contains some details the others omit. It is important to note the date of the funeral as being Monday 2nd January 1815, as it is often incorrectly stated as taking place on 1st January (even by some scholars).

Burial of the wicked Joanna.

After the dissection on Saturday se’nnight, the body was put in a plain coffin by the Undertaker’s men, in the presence of three Gentlemen. From the putrefaction which had taken place, the smell was most intolerable. In consequence, when the lid was screwed down, pitch was applied to the edges and rim, to confine and prevent the egress of the misserata. While this was performing, the strictest injunctions of secrecy were given to all present. At twelve o'clock on the same night, the crowd having retired from the street, the coffin was carried by four men to Mr. Moore’s, the undertaker, corner of Rathbone place, Oxford-street. Here it remained during Sunday. On Monday afternoon, about two o'clock, it was put into a hearse, drawn by two horses, without the usual ornament of feathers, to favour the belief, had it been recognized, that it did not contain a corpse, but was only going to receive and convey one. The hearse, followed by three gentleman in a coach and pair, then proceeded to Marylebone Upper Burying-ground, near Kilburn, where it was interred; and the usual Church service repeated by the Clergyman. The few people whom curiosity attracted round the grave had not the slightest suspicion that the coffin which was lowering down contained the remains of Joanna Southcott. In fact such precautions were taken, that it was impossible that the secret could prematurely transpire.—It was known to none of her followers, and scarcely to any of her late confidants. The three Gentleman who followed the corpse to the grave were muffled up more than is customary even to mourners: they wore great coats, which were buttoned up to the chin, black cloaks standing high in the collar, handkerchiefs tied round the lower part of the face, and their hats pulled over their eyes. So completely had they succeeded in disguising themselves, that not a feature was visible: they abstained from all conversation, so that the writer of this communication could not recognize their persons. On their road to the place of interment, they were joined by a fourth person, equally well disguised as themselves, and who did not separate from them. This last is conjectured to have been Tozer.

The Morning Post of 16th January 1815 recorded an 'altercation' between the officiating Clergyman at the funeral and William Tozer, one of Southcott's disciplines, having taken place:

Tozer complained the the regular Church Service had not been gone through; the Clergyman replied that the customary prayer for the dead had been read. Tozer said this was not sufficient for so holy a woman and a prophetess! to which the Clergyman replied, that he trusted it would never again be his lot to officiate at the funeral of one who had lived by practising imposture and fraud, uttering blasphemes, and died unrepentant. This severe remark but just silenced Tozer.

The grave at St John's Wood burial ground in London features both an old and new headstone. The old burial stone is recumbent and covers the grave, but is damaged, with most of the original inscription obscured. The stone doesn't seem to have been erected immediately, with newspapers first commenting upon it in May 1815 (in particular the Morning Chronicle of 29th May 1815 which I consulted), nearly 5 months after the funeral. Photos of this stone can be seen here and here.

A much finer tablet was erected in 1828, along the wall of the cemetery directly in front of the old burial stone. Contemporary newspaper articles (the Sheffield Independent of 27th December & York Herald of 18th October 1828) remark that it was made from black marble, edged in white, with gold lettering and stars in silver next to the word 'Sacred' at the top. This headstone was damaged (allegedly by an explosion on a nearby barge carrying gunpowder in 1874), and replaced by the latest one - pictured above - in 1965 by the Panacea Society.